"Greetings Mr. Lukeman: For the sake of argument, let's just say I have a body of humorous non-fiction stories, well-written essays that comprise more than enough laugh-out-loud moments to capture the attention of an agent and/or publisher. Let's say I have enough material for several books and I'm the kind of author who's central character (in other words, his own personality) could be rendered for marketing purposes, much in the same way the "character" of David Sedaris is central to most of his work. (And please forgive me for being yet another one of the thousands of aspiring authors who directly or indirectly compare themselves to David Sedaris...) Once again I'll ask you to play along with me and pretend, for the moment, I'm the next great American icon of literature, as of yet undiscovered. Here's the question: should I submit one or more of these stories first to magazines for hopeful publication, or should I bypass that route and submit them (to an agent) as a full book?"
There is no black and white answer to this. On the one hand, if you are successful in landing one of your stories in a major, national publication, like the New Yorker, then yes, that can make all the difference in the world. On the other hand, if you are only able to land your story in a lesser known publication, that may end up not having any impact – and indeed, if you land your stories in too many publications, it could even potentially turn off an agent or editor, because they might feel as if the book has been over serialized, and overexposed.
The other issue is that if you submit your stories to all the major publications, and they all reject you, you've lost your one shot. It is possible that if an agent had submitted the same story, or a sub rights director at a publishing house, perhaps the same publications would have accepted your story. Unfortunately, who is doing the submitting can often make a big difference in how seriously your story is paid attention to.
But then again, agents rarely have time to submit individual stories to magazine, and the same is true with rights departments. It all depends on the book. For some authors, sub rights are very big deal, and a single story can demand six figures in a publication. But for the vast majority of authors, they will never sell serial rights, and if they do, it will be to a lesser publication, and for a nominal fee of a few hundred dollars. That is why it is hard to make blanket generalizations.
The other consideration is that it could take you many many months of trying to place your stories in magazines, and one does not want to put on hold his career or his search for an agent too long. Especially because the chances of your landing your stories in a place that can actually impact an agent's decision, like the New Yorker, are very slim. And you don't want to spend so many months to finally land your stories in lesser magazines, and then search for an agent only to discover that even these small successes will not impact the agent's decision.
Thus I would recommend just submitting directly to agents, and not waiting on magazines. If your writing is good enough, the agent should want to take it on anyway. And if it is not good enough, then landing a piece likely will not make much of a difference. Of course, if you have exhausted your agent search, and the manuscript is sitting there, you can always try the magazines then. And if you do land one in a major place, then you can reapproach the agents.
Also keep in mind that in this day and age, there are many ways to approach it. Some websites can have even more impact than magazines--if you get millions of reads on a site, that can influence an agent's decision. Or if you break your humor into tweets and have millions of followers, that can make the difference, too.